We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

ISEE Upper Level Math : Operations

Study concepts, example questions & explanations for ISEE Upper Level Math

Create An Account

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 7 Next →

Example Question #11 : How To Multiply Variables

Simplify:

$(-\frac{5}{3})^{-3}$

Possible Answers:

$-\frac{125}{27}$

$\frac{125}{27}$

$-\frac{27}{125}$

$-\frac{25}{9}$

$\frac{27}{125}$

Correct answer:

$-\frac{27}{125}$

Explanation:

First, recognize that raising the fraction to a negative power is the same as raising the inverted fraction to a positive power.

$(-\frac{5}{3})^{-3}=(-\frac{3}{5})^3$

Apply the exponent within the parentheses and simplify. The negative in the fraction can be applied to either the numerator or the denominator, but not both; we will apply it to the numerator.

$\frac{(-3)^3}{(5)^3}$

$\frac{-27}{125}=-\frac{27}{125}$

The fraction cannot be simplified further.

Report an Error

Example Question #11 : How To Multiply Variables

Solve for $\dpi{100} x$ :

$\dpi{100} \frac{1}{3}x-14=7$

Possible Answers:

$\dpi{100} 63$

$\dpi{100} 7$

$\dpi{100} 3$

$\dpi{100} 21$

Correct answer:

$\dpi{100} 63$

Explanation:

$\dpi{100} \frac{1}{3}x-14=7$

$\dpi{100} \frac{1}{3}x-14+14=7+14$

$\dpi{100} \frac{1}{3}x=21$

$\dpi{100} 3\cdot \frac{1}{3}x=21\cdot 3$

$\dpi{100} x=63$

Report an Error

Example Question #901 : Isee Upper Level (Grades 9 12) Mathematics Achievement

If the product of three consecutive numbers is 990, what is the smallest number?

Possible Answers:

Correct answer:

Explanation:

If the product of three consecutive numbers is 990, then the smallest number can be found by plugging in each answer choice into the scenario to see whether it is correct.

If we plug in 9 as the smallest number, then the two consecutive numbers would be 10 and 11.

Given that 9 times 10 times 11 equals 990, that is the correct answer.

Report an Error

Example Question #14 : How To Multiply Variables

What is the simplified version of the expression below?

$(\frac{5}{4}\cdot8+6\div3)^{2}-12$

Possible Answers:

132

Correct answer:

132

Explanation:

The first step is to simplify the values in the parentheses:

$(\frac{5}{4}\cdot8+6\div3)^{2}-12$

$(10+2)^{2}-12$

$12^{2}-12$

144-12

132

Report an Error

Example Question #11 : Operations

Simplify:

$4xy^2-2xy+y^{2}x+y^3-8xy+4yx$

Possible Answers:

5xy^2-6xy+y^3

xy^2-4xy+y^3

4xy^2-10xy+y^3

4xy^2-6xy+y^3

4xy^2-10xy+yx^2+y^3+4yx

Correct answer:

5xy^2-6xy+y^3

Explanation:

Reorder the expression to group like-terms together.

$4xy^2-2xy+y^{2}x+y^3-8xy+4yx$

$(4xy^2+y^{2}x)+(-2xy+-8xy+4yx)+y^3$

Simplify by combining like-terms.

Report an Error

Example Question #16 : How To Multiply Variables

If $x^{2}-12x$ is a positive number, what is a possible value of ?

Possible Answers:

Correct answer:

Explanation:

If x is equal to , then the equation could be written as follows:

$x^{2}-12x$

$-4^{2}-(12*-4)$

16+48=64

Given that is a positive number, is a possible value of .

Report an Error

Example Question #17 : How To Multiply Variables

Megan teaches a cooking class. Every time a student takes a class, the student receives a 10% discount off of the price he paid for the previous class. The first class that Jose took cost $50. What will be the first class in which Jose pays less than $38?

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, the price of $50 must be discounted by 10% until we get to a price of $38 or less.

The first class is 50.

The second class, being 10 percent less than the previous one, is $50-.1\cdot 50=50-5=45$

The third class, being 10 percent less than the previous one, is $45-.1\cdot45=45-4.5 = 40.5$

The fourth class, being 10 percent less than the previous one, is $40.5-.1\cdot40.5=40.5-4.05=36.45$

Therefore, the answer is 4.

Report an Error

Example Question #18 : How To Multiply Variables

Simplify the following expression

(6x^2)*(3x^3)

Possible Answers:

18x^5

18x^6

9x^6

9x^5

Correct answer:

18x^5

Explanation:

Simplify the following expression

(6x^2)*(3x^3)

Let's begin by multiplying our coefficients:

6*3=18

Next, we need to realize that we can combine our x's by adding the exponents.

$x^2*x^3=x^{3+2}=x^5$

Put it all together to get:

18x^5

Report an Error

Example Question #19 : How To Multiply Variables

Simplify the following:

(9q^3n^3)(q^5n^6)

Possible Answers:

9q^8n^9

9q^9n^8

$9qn^{72}$

81q^8n^9

Correct answer:

9q^8n^9

Explanation:

Simplify the following:

(9q^3n^3)(q^5n^6)

To begin, our coefficient will not change. We have just one integer (the 9) and nothing to multiply it by.

To combine our exponents, we will add them. This is because we are multiplying them

$q^3*q^5=q^{3+5}=q^8$

$n^3*n^6=n^{3+6}=n^9$

Put it together to get:

9q^8n^9

Report an Error

Example Question #20 : How To Multiply Variables

$x^{2} = 18$

$y^{2} = 2$

and are both positive.

Evaluate (2x+ 3y) (3x-2y) .

Possible Answers:

150

126

Correct answer:

126

Explanation:

Multiply the binomials using the FOIL method - first, outer, inner, last - then combine like terms:

(2x+ 3y) (3x-2y)

$= 2x \cdot 3x - 2x \cdot 2y+ 3y \cdot 3x-3y \cdot 2y$

$=6 x ^{2}-4 x y+ 9xy-6y^{2}$

$=6 x ^{2}+ 5 xy-6y^{2}$

$x^{2} = 18$ and $y^{2} = 2$ ; also, by the Power of a Product Principle:

$(xy) ^{2} = x^{2}y^{2}$ .

and are both positive, so, substituting:

$xy = \sqrt{x^{2}y^{2}} = \sqrt{18 \cdot 2} = \sqrt{36} = 6$ .

Again, using substitution:

(2x+ 3y) (3x-2y)

$=6 x ^{2}+ 5 xy-6y^{2}$

=6 (18)+ 5 (6)-6 (2)

=108 +30-12

=126

Report an Error

← Previous 1 2 3 4 5 6 7 Next →

View Tutors

Tynisha
Certified Tutor

Georgia State University, Bachelor in Arts, Political Science and Government. Thomas M Cooley Law School, Juris Doctor, Busin...

View Tutors

Jaroslaw
Certified Tutor

Heriot Watt University, Master of Science, Physics. Heriot Watt University, Doctor of Science, Theoretical and Mathematical P...

View Tutors

Joseph
Certified Tutor

University of Waterloo, Doctor of Philosophy, Applied Mathematics.

All ISEE Upper Level Math Resources

6 Diagnostic Tests 244 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GRE Tutors in San Francisco-Bay Area, French Tutors in Atlanta, Algebra Tutors in Philadelphia, Reading Tutors in Houston, LSAT Tutors in Dallas Fort Worth, GRE Tutors in Atlanta, Biology Tutors in San Francisco-Bay Area, SSAT Tutors in Denver, ACT Tutors in Dallas Fort Worth, Chemistry Tutors in Phoenix

Popular Courses & Classes

SAT Courses & Classes in Chicago, SSAT Courses & Classes in San Francisco-Bay Area, Spanish Courses & Classes in Boston, SAT Courses & Classes in San Diego, Spanish Courses & Classes in Denver, SSAT Courses & Classes in Phoenix, GMAT Courses & Classes in Philadelphia, ISEE Courses & Classes in Boston, MCAT Courses & Classes in Atlanta, GMAT Courses & Classes in Denver

Popular Test Prep

ACT Test Prep in Boston, MCAT Test Prep in Washington DC, SAT Test Prep in Miami, ISEE Test Prep in Washington DC, SAT Test Prep in Chicago, LSAT Test Prep in Dallas Fort Worth, GRE Test Prep in Houston, SSAT Test Prep in San Francisco-Bay Area, LSAT Test Prep in Los Angeles, GRE Test Prep in Boston

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

ISEE Upper Level Math : Operations

Study concepts, example questions & explanations for ISEE Upper Level Math

All ISEE Upper Level Math Resources

Example Questions

Example Question #11 : How To Multiply Variables

Example Question #11 : How To Multiply Variables

Example Question #901 : Isee Upper Level (Grades 9 12) Mathematics Achievement

Example Question #14 : How To Multiply Variables

Example Question #11 : Operations

Example Question #16 : How To Multiply Variables

Example Question #17 : How To Multiply Variables

Example Question #18 : How To Multiply Variables

Example Question #19 : How To Multiply Variables

Example Question #20 : How To Multiply Variables

All ISEE Upper Level Math Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: